Rear end clunking going over small bumps

I have 1 1993 Toyota Corolla with over 200,000 miles on it. Recently it has started making a severe clunking noise from the rear passenger side when going over even small bumps in the road and the ride has become very rough. When I push down on the rear driver side there is bounce. When I push down on the rear passenger side there is no give at all. What's gone wrong?